We show that our approach can offer several important advantages, both theoretical and practical. First, it provides a significant gain in terms of estimation efficiency, as it allows us to estimate multiple VaR and ES in just one step. Second, it can significantly improve blackforecasts accuracy, since it accounts for the dependence structure among financial assets, that cannot be detected by univariate methods.
These results are also confirmed empirically. Indeed, using three stock
market indices as in [1]}, we estimate the pairs of (VaR, ES) for each of the three assets and evaluate the forecasts using a new scoring function based on the MAL density, which allows us to account for the dependence structure among the considered assets at each point in time. The forecasts of VaR and ES have been compared with the ones obtained by the univariate approach of [1]}, i.e. by considering the three stock market indices separately, as they were independent to each other. What we find is a significant gain in terms of forecasting accuracy using the proposed multivariate framework, leading to more reliable risk measure estimates.
